Question

Is the number 1 rational or irrational?

Answer 1

Rational

Explanation:

A rational number is one that can be expressed as a fraction of integers. For instance, we can express the number 1 in an infinite number of ways:

`1/1, 2/2, 3/3, (-1)/(-1)`

In fact, any integer divided by itself will give us 1.

An irrational number is one that cannot be expressed as a fraction of two integers. For instance, the most famous of irrational numbers is `pi` - the ratio of a circle's circumference to its diameter. As an approximation, `pi` is sometimes expressed as `3.14` or `22/7`, but in actuality the decimal runs forever, never repeating and never ending.

Answer 2

The number 1 can be classified as: a natural number, a whole number, a perfect square, a perfect cube, an integer.

This is only possible because `1` is a RATIONAL number.

Explanation:

Once a number is irrational, that's it. It cannot be classified further.

However,`color(magenta)(" rational")` numbers can be classified into different types of numbers.

A rational number is defined as 'A number which can be written in the form `color(magenta)(p/q)` where `p and q` are integers, but `q !=0`

Some rational numbers become integers, some remain as fractions:

Integers:`30/5, 12/4, -9/3, color(magenta)(7/7), 0/8` Fractions: `2/3, 15/4, 1/7`

Some integers are negative, the rest are whole numbers.

Whole numbers include `{0,color(magenta)(1),2,3,4,5,6,......}`

Whole numbers can be broken down into 0 and natural numbers.

Natural numbers include `{color(magenta)(1)(,2,3,4,5,6...}`

Within the natural numbers you will also have different types of numbers, including odds, evens, primes, composites, perfect squares, perfect cubes, etc.

The number `color(magenta)(1)` can be classified as: a natural number, a whole number, a perfect square, a perfect cube, an integer.

This is only possible because it is a rational number.

Note that `color(magenta)(1)` is not prime because it has only one factor.